The cerebral cortex is composed of very large numbers of interconnected neurons extended layers, as are the sensory receptors in the eye, ear, nose and skin. The signals transmitted by receptors to cortex are spatial patterns of nerve impulses. We infer that neural activity in the cerebral cortex resulting from sensory signals also exists in spatial patterns. Experiments to test this hypothesis require simultaneous recording of neural electrical activity from spatial arrays of electrodes placed on the cortex of normally behaving animals. Initial tests of the hypothesis in the sensory system for olfaction have shown that the spatial patterns of neural activity in the olfactory parts of the cortex do not depend on the on-going stimulus. Instead they depend on the past experiences of animals with the stimulus. We infer that the cortical electrical patterns are determined by a state of search by an animal, and manifest the mental image of an odor that an animal creates as the basis for its search. We propose to test the hypothesis by recording the olfactory brain waves of rabbits and cats that have been trained to expect particular odors, and to measure the changes in spatial brain wave pattern that occur as the expectation is created by training, and as the expected odor is actually delivered.